Tubular-type heat-exchange apparatus

ABSTRACT

Heat-exchange apparatus of a kind wherein a substance is heated by the flow of a hot gaseous fluid through a series of like, spaced, parallel flues which pass through the substance to be heated and wherein each of the parallel flues communicates at one end with a supply flue and at its opposite end with a delivery flue, and wherein the supply and delivery flues are so relatively arranged and are so proportioned, as to relative transverse area from point-to-point, that an equal quantity of the gaseous fluid flows through each of the parallel flues per unit of time.

United States Patent TUBULAR-TYPE HEAT-EXCHANGE APPARATUS 5 Claims, 4Drawing Figs.

U.S. C1 165/175,

122/155, 165/1 Int. Cl F28f 9/00 Field of Search... 165/ l 74,

[56] References Cited FOREIGN PATENTS 192,936 11/1957 Austria 165/1751,396,215 3/1965 France 165/175 Primary Examiner-Albert W. Davis, Jr.Attorney-Roberts, Cushman & Graver ABSTRACT: Heat-exchange apparatus ofa kind wherein a substance is heated by the flow of a hot gaseous fluidthrough a series of like, spaced, parallel flues which pass through thesubstance to be heated and wherein each of the parallel fluescommunicates at one end with a supply flue and at its opposite end witha delivery flue, and wherein the supply and delivery flues are sorelatively arranged and are so proportioned, as to relative transversearea from point-to-point, that an equal quantity of the gaseous fluidflows through each of the parallel flues per unit of time.

TUBULAR-TYPE HEAT-EXCHANGE APPARATUS This invention relates toheat-exchange apparatus, for specific example, a parallel-flue boilerhaving a plurality of parallel flues spaced from each other and whichare of the same transverse cross-sectional area, each of whichcommunicates at one end with a supply flue and at the other end with adelivery or discharge flue. For heating efficiency an equal quantity ofthe gaseous heating fluid should pass through each of the parallel fluesper unit of time, and this means that the pressure differential betweenthe receiving and delivery ends of each respective one of the parallelflues must be alike, but this high efficiency is not attained incustomary devices of this type wherein the supply and delivery flues areof the same diameter and in which the gaseous heating fluid flows in thesame direction through the supply and the delivery flues.

This lack of efficiency is due, primarily, to the fact that the severalflues do not conduct the same quantity of gas per unit of time.

The object of the present invention is to provide heatexchange apparatusof the parallel-flue type and of such construction that the totalquantity of the heating gas which passes through the apparatus, per unitof time, will be equally distributed among the several parallel flues.

For convenience in description but without limiting in text, the heatingfluid, which would usually be a gaseous product of combustion, and thusa gaseous fluid, will herein be referred to merely as gas."

ln the accompanying drawing:

FIG. 1 is a diagrammatic vertical section, in a plane which passesthrough the axes of the parallel flues, illustrating a fiveflue boileraccording to the present invention;

FIG. 2 is a diagram illustrative of the comparative quantity of gaswhich passes, per unit of time, through the several parallel flues;

FIG. 3 is a view similar to FIG. 1, but showing a conventional boiler ofthe usual type; and

H0. 4 is a diagram, similar to FIG. 2 showing the relative amount of gaswhich passes trough the several flues of the boiler of FIG. 3.

One unfamiliar with apparatus of this type, in looking at FIG. 3, whichillustrates a boiler of conventional type, would expect that fluidentering the supply flue S at X and passing through the parallel fluesto the discharge flue D, would divide itself equally between the severalparallel flues, but this would not be truev What' actually would occurwould be that the first of the series of parallel tubes (that is thetube nearest to the intake point X, would carry the least amount of gas,while the last of the series would carry the greatest quantity.

This result is because of the dynamic pressure increase between theinlet end 1 of the supply flue and the dead end 5 of the supply flue,and the dynamic pressure loss between the points 6 and 10 of thedischarge flue.

Assuming that the pressure at the point 1 is P, and the dynamic pressureof the entering gas at the point 1 is represented by the expressionA,V,/2gc, (where Ais the density of the gas) then. since the velocity Vdecreases approximately to zero at the point 5, (because of the loss ofgas through the several parallel flues) and because of the resultantconversion of kinetic energy into pressure, the pressure at the point 5is represented by the expression P,+A, Vfi/Zgc On the contrary, in thedischarge flue, the velocity will increase from the point 6 to the point10, (because of the influx of gas along the discharge flue D) so teatthe pressure differential between the points 5 and 10 will exceed thepressure differential between the points 1 and 6 by 517%;- Ami 2, Zgc

Thus the flow rate in the last of the parallel flues (between the points5 and 10) will exceed the flow rate between points 4 and 9, etc., untilthe lowest flow rate will be from 1 to 6. This nonuniform distributionof hot gas is graphically illustrated in FIG. 4. v

By rearranging the discharge flue D as shown in FIG. 1, and by properlyproportioning the cross-sectional areas of the supply and dischargeflues S and D, the pressure drop along each of the parallel flues may bemade equal.

Referring to FIG. 1, if the density of the gas at the inlet point X andat the discharge point Y, were equal, then the transverse areas at thosepoints should be equal so that P,,P,=A,V /2gc while P,,,P =A, V,"'/2gcwhich would assure thatP,-P P,P,,,. Similarly, it may be shown that allof the parallel flues would show the same pressure differential andtherefore have equal flow rates.

in proof of the possibility of attaining the above results, certainassumptions based on observed facts may be made.

In a heat exchanger such as a boiler or furnace, the temperature of thehot gas, entering the supply flue S at the point X would be higher thanthat of the gas leaving the discharge flue D at the point Y. Forexample, the temperature of combustion products of a burner, entering atX would normally be approximately 3,200 F., and it may be assumed thatthe temperature of the gas at the points 1, 2, 3, 4 and 5, of the supplyflue S would be about the same. Assuming that the flow rate of the gasthrough each of the parallel flues is the same, the temperature at eachof the points 10, 9, 8, 7 and 6 of the delivery flue D would be nearlyequal and probably approximately 400 F.

The density of the gas at the points Y, 6, 7, 8, 9 and 10 would begreater than at the points X, l. 2, 3, 4 and 5, in an inverse ratio tothe absolute temperatures.

Thus, for example, and employing the symbol A as indicating density, andTindicating absolute temperature,

in order to maintain equal pressure differentials through each of theparallel flues, it is necessary that the-dynamic pressure at the points1 and 6; 2 and 7-5 and 10, etc. be equal, that is to say l A,V,=A,V,,etc.

Since under a steady-flow condition, the entire mass flow entering at Xand leaving at Y is the same, and designating the transverse area of theflue S by the character N, at the point 1, and the transverse area atthe point 6 by N -then N, would equal N and A,N, V,=A,,N,, V

Now referring to equations l and (2) supra,

L5 A, V.,

Then

- a N6 Al and In the example above cited l Then by making the transverseflue areas N, and N,,, at the points 1 and 6, respectively, inaccordance with the formula equal, and in the same way the dynamicpressure at thepoints 2 and 7, 3 and 8, etc. will be equal.

For instance, with five parallel flues as shown in FIG. 1 and eachcarrying one-fifth of the totalvolume of flow, the axial velocity V =0.8V,, and the axial velocity V =0,8 V Since T,= T and Tan, etc.

Then A,=A, and A =A etc.

Substituting in equation l) A,V, A,,V,, A V, =A V A V, /0.8=A, V,,'-/0.8

A, V =A-, V Likewise A V A V etc Thus, by arranging the supply anddischarge flues so thatgas flows in opposite directions and byproportioning the supply flue S and the discharge flue D according tothe equation N n l where n represents any number of parallel flues; aboiler may be manufactured wherein the flow through each of the parallelflues will be the same.

What I claim is:

l. A heat exchanger comprising spaced parallel flues of uniform crosssection, one of which constitutes a supply flue and the other adischarge flue, and a plurality of spaced parallel transfer fluessituated between the supply and discharge flues with the ends of each ofthe transfer flues connected with the supply and discharge flues andperpendicular thereto, the supply and discharge flues having inlet andoutlet openings and being positioned with the inlet and outlet openingsat the same end so that the gas entering the inlet opening of the supplyflue flows along the supply flue, then through the transfer flues, theninto and along the discharge flue and finally out through outlet openingso as to reverse the gas flow; characterized in that the cross sectionof the discharge flue is less than that of the supply flue in suchproportion that the heated gas which enters the supply flue is dividedequally among the several parallel flues on its way to the dischargeflue.

2. A heat exchanger comprising spaced parallel flues of uniform crosssection, one of which constitutes a supply flue and the other adischarge flue and n spaced parallel transfer flues arranged with theiraxes perpendicular to the axes of the supply and discharge flues andwith their ends in communication with the supply and discharge flues,the supply and discharge flues having inlet and outlet openings andbeing positioned with the inlet and outlet openings at the same end sothat the gas entering the inlet opening of the supply flue flows alongthe supply flue, then through the transfer flues,

then into and along the discharge flue and'finally out through outletopening so as to reverse the gas flow, said inlet and outlet openingscomprising open ends preceding the first of the n spaced transfer fluesand closed ends following the last of the n spaced transfer flues, andwherein the cross-sectional area of the discharge flue is less than thecross-sectional area of the supply flue in such proportion that at theintersections of the opposite ends of each one of said n transfer flueswith the supply and discharge flues, respectively, the dynamic pressureof the heated gas is the same.

3. The combination according to claim 2, wherein there are n parallelflues; characterized in that the cross-sectional areas N, and N of thesupply and discharge flues are proportioned in accordance with theformula a 1- n I where A, is the density of the hot gas where it entersthe first of the parallel flues, and A is the density of the gas whereit leaves the n"' flue of the series.

4. The combination according to claim 2, and wherein there are five ofthe parallel flues, and wherein the gas enters the supply flue at atemperature of approximately 3,200 F. and leaves the discharge flue at atemperature of approximately 400 F., and wherein the cross-sectionalareas N, and N of the supply and discharge flues at their inlet andoutlet ends, respectively, are proportioned in accordance with theformula N,/N=2.07.

5. The combination, according to claim 2, further characterized in thatthe transverse area N, of the supply flue is related to the transversearea of the discharge flue in accordance with the formula & a

where T, and T, are the absolute temperatures, at the entrance end ofthe supply flue and the delivery end of the discharge flue,respectively,

1. A heat exchanger comprising spaced parallel flues of uniform cross section, one of which constitutes a supply flue and the other a discharge flue, and a plurality of spaced parallel transfer flues situated between the supply and discharge flues with the ends of each of the transfer flues connected with the supply and discharge flues and perpendicular thereto, the supply and discharge flues having inlet and outlet openings and being positioned with the inlet and outlet openings at the same end so that the gas entering the inlet opening of the supply flue flows along the supply flue, then through the transfer flues, then into and along the discharge flue and finally out through outlet opening so as to reverse the gas flow; characterized in that the cross section of the discharge flue is less than that of the supply flue in such proportion that the heated gas which enters the supply flue is divided equally among the several parallel flues on its way to the discharge flue.
 2. A heat exchanger comprising spaced parallel flues of uniform cross section, one of which constitutes a supply flue and the other a discharge flue and n spaced parallel transfer flues arranged with their axes perpendicular to the axes of the supply and discharge flues and with their ends in communication with the supply and discharge flues, the supply and discharge flues having inlet and outlet openings and being positioned with the inlet and outlet openings at the same end so that the gas entering the inlet opening of the supply flue flows along the supply flue, then through the transfer flues, then into and along the discharge flue and finally out through outlet opening so as to reverse the gas flow, said inlet and outlet openings comprising open ends preceding the first of the n spaced transfer flues and closed ends following the last of the n spaced transfer flues, and wherein the cross-sectional area of the discharge flue is less than the cross-sectional area of the supply flue in such proportion that at the intersections of the opposite ends of each one of said n transfer flues with the supply and discharge flues, respectively, the dynamic pressure of the heated gas is the same.
 3. The combination according to claim 2, wherein there are n parallel flues; characterized in that the cross-sectional areas N1 and Nn of the supply and discharge flues are proportioned in accordance with the formula where Delta 1 is the density of the hot gas where it enters the first of the parallel flues, and Delta n is the density of the gas where it leaves the nth flue of the series.
 4. The combination according to claim 2, and wherein there are five of the parallel flues, and wherein the gas enters the supply flue at a temperature of approximately 3,200* F. and leaves the discharge flue at a temperature of approximately 400* F., and wherein the cross-sectional areas N1 and N6 of the supply and discharge flues at their inlet and outlet ends, respectively, are proportioned in accordance with the formula N1/N6 2.07.
 5. The combination, according to claim 2, further characterized in that the transverse area N1 of the supply flue is related to the transverse area of the discharge flue in accordance with the formula where T1 and T6 are the absolute temperatures, at the entrance end of the supply flue and the delivery end of the discharge flue, respectively. 